Calculating the norm matrix to solve the A-body Schr\"odinger equation within a set of non-orthogonal many-body states

Abstract

There are efficient many-body methods, such as the (symmetry-restored) generator coordinate method in nuclear physics, that formulate the A-body Schr\"odinger equation within a set of nonorthogonal many-body states. Solving the corresponding secular equation requires the evaluation of the norm matrix and thus the capacity to compute its entries consistently and without any phase ambiguity. This is not always a trivial task, e.g. it remained a long-standing problem for methods based on general Bogoliubov product states. While a solution to this problem was found recently in Ref. [L. M. Robledo, Phys. Rev. C79, 021302 (2009)], the present work introduces an alternative method that can be generically applied to other classes of states of interest in many-body physics. The method is presently exemplified in the case of Bogoliubov states and numerically illustrated on the basis of a toy model.

Comment: 5 pages, 2 figures